论文标题
循环组和QNEC
Loop Groups and QNEC
论文作者
论文摘要
我们研究了循环组模型的一些分析属性，表明循环组$ lg $的正能表示（PER）可以扩展到$ h^{3/2}}（s^1，g）$的每个紧凑，简单且简单连接的Lie Group $ G $。然后，我们明确计算应力能量张量对$ H^{5/2}（s^1，g）$的伴随动作，我们使用这些结果证明量子无效的能量条件（QNEC）和Bekenstein绑定了通过将Sobolev循环涂在真空吸尘器上获得的状态。我们还提供了更简单的证明，证明了$ g = su（n）$中的这些最后结果。最后，我们构建和研究了循环集团的共形网的孤子表达，这是由循环通过$ -1 $不连续的循环引起的。
We investigate some analytical properties of loop group models, showing that a Positive Energy Representation (PER) of a loop group $LG$ can be extended to a PER of $H^{3/2}(S^1,G)$ for any compact, simple and simply connected Lie group $G$. We then explicitly compute the adjoint action of $H^{5/2}(S^1,G)$ on the stress energy tensor and we use these results to prove the Quantum Null Energy Condition (QNEC) and the Bekenstein Bound for states obtained by applying a Sobolev loop to the vacuum. We also give a simpler proof of these last results in the case $G=SU(n)$. Finally, we construct and study solitonic representations of the loop group conformal nets induced by the conjugation by a loop with a discontinuity in $-1$.
